2 of 2 added source link, removed fluff, minor grammar up-sprucing

What's the meaning of “gun shy” and “come back in here”?

From NPR:

One problem we would have here is to calculate the damage because I believe the damage is incalculable and it's going to ripple into the future, because it will cost us convention business and people will be a little gun shy about coming back in here if they think this could happen again.

I have two questions:

  1. What's the meaning of gun shy?
  2. come back in here is a little weird for me. I know a phrase is come here, so I think if I want to stress the orientation back, I can only add a word back before here, just as come back here (but still a little weird for me). So why does he add the word in before here? Can you give me more examples?